The field of the invention is nuclear magnetic resonance methods and systems. More particularly, the invention relates to the design of RF pulses used in nuclear magnetic resonance ("NMR") spectroscopy and magnetic resonance imaging ("MRI") pulse sequences.
When a substance such as human tissue is subjected to a uniform magnetic field (polarizing field B.sub.0), the individual magnetic moments of the spins in the tissue attempt to align with this polarizing field, and the component of net magnetization perpendicular to the polarizing field precess about it at the characteristic Larmor frequency. If the substance, or tissue, is subjected to an RF magnetic field (excitation field B.sub.1) which is in the x-y plane and which is near the Larmor frequency, the net aligned moment, M.sub.z, may be rotated, or "tipped", into the x-y plane to produce a net transverse magnetic moment M.sub.t. A signal is emitted by the excited spins, and after the RF excitation signal B.sub.1 is terminated, this signal may be received and processed to form an image.
When utilizing these signals to produce images, magnetic field gradients (G.sub.x G.sub.y and G.sub.z) are employed. Typically, the region to be imaged is scanned by a sequence of measurement cycles in which these gradients vary according to the particular localization method being used. The resulting set of received NMR signals are digitized and processed to reconstruct the image using one of many well known reconstruction techniques.
There are numerous pulse sequences used in MRI and in NMR spectroscopy. These pulse sequences use at least one, and usually more than one, RF pulse near the Larmor frequency. In addition to the RF excitation pulse mentioned above, such RF excitation pulses may, for example, invert spin magnetization, saturate spin magnetization, stabilize spin magnetization or refocus spin magnetization. When used in combination with a magnetic field gradient, the RF pulses selectively affect spin magnetization over a specific frequency range which corresponds to a specific location within the subject being scanned. Such "selective" RF pulses are thus specified by the degree to which they tip magnetization ("flip-angle") over a range of frequencies.
In U.S. Pat. No. 4,940,940 a method is disclosed for designing RF pulses that will produce a desired flip-angle over a specified frequency range. The disclosure of this patent is hereby incorporated by reference. This method, known in the art as the "SLR" method, starts with the desired frequency domain pulse profile (for example, a 90.degree. flip-angle over a specified slice thickness/frequency range) and calculates the amplitude and phase of an RF pulse, that when played out over time, will produce the desired result. These calculations involve the approximation of the desired frequency domain pulse profile with two high order polynomials A and B which can then be transformed directly into an RF pulse that is "played out" on an NMR system. The step of producing the polynomials A and B employs a Remez (Park-McClellan) algorithm that is executed in an iterative process. To calculate the necessary A and B polynomials (hereinafter referred to as the "SLR polynomials") this iterative process is performed until the desired frequency domain pulse profile is approximated to a specified degree of accuracy.
In MR imaging, almost every scan involves the construction of images of multiple slices. This is commonly done with conventional multi-slice imaging, in which the actions necessary to acquire the data from each slice are interleaved within a single repetition time (TR). Alternatively, when the number of desired slices is large, it is possible to perform 3D Fourier imaging, in which the through-slice direction is phase encoded. When the desired number of slices is small, but conventional multi-slice imaging requires multiple passes, either because of a short TR or because data acquisition for a particular slice is long (e.g. echo planar or spiral acquisition), an alternative to the two standard methods described above provides a significant signal to noise improvement. This method uses "multiband excitation" in which multiple bands of magnetization are excited simultaneously with a single radiofrequency (RF) pulse. Imaging methods that make use of multiband RF pulses includes POMP, Hadamard encoding, and wavelet encoding.
Conventionally, the RF pulses for a multiband method are made by summing the separate RF pulses needed to excite each slice separately. There are many methods for designing the separate RF pulses, including the SLR method described in the above-cited patent. This method of multiband RF pulse construction works well only when the excited slices are separated by an adequate gap. The "composite" RF pulse must excite regions separated by a gap in order to avoid slice interference when the slices are close together. Another problem related to multiband excitation stems from a phase error that depends on the position of the excited band. This so-called band-position phase error arises when a slice is excited off-resonance by applying a phase ramp to the RF pulse envelope. A phase ramp occurs when each sample of the RF pulse envelope is multiplied by a complex number of unit magnitude and a phase that depends linearly on the sample index. This phase error can be corrected by multiplying each RF pulse sample by a complex number whose phase is the negative of the band-position phase error. The actual phase correction depends on many factors related to the particular RF pulse.